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Wave Optics
Resolving Power of Telescope
1 question from 1 paper, each with its answer.
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Concepts tested
- Limit of resolution of telescope
All Questions
2004 AIPMT 1 question
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A telescope has an objective lens of 10 cm diameter and is situated at a distance of one kilometer from two objects. The minimum distance between these two objects, which can be resolved by the telescope, when the mean wavelength of light is 5000 Å, is of the order of-
Let d be the separation of the two objects and D their distance from the telescope. The angle they subtend at the objective is $\theta = \dfrac{d}{D}$.
The limit of resolution of a telescope with aperture a is $\theta \approx \dfrac{\lambda}{a}$ (the exact relation is $\theta = \dfrac{1.22\lambda}{a}$, but only the order of magnitude is asked).
For just resolving: $\dfrac{d}{D} = \dfrac{\lambda}{a} \Rightarrow d = \dfrac{\lambda D}{a}$
$\lambda = 5000$ Å $= 5000 \times 10^{-10}$ m, $D = 1$ km $= 10^3$ m, $a = 10$ cm $= 10 \times 10^{-2}$ m
$d = \dfrac{5000 \times 10^{-10} \times 10^3}{10 \times 10^{-2}} = 5 \times 10^{-3}$ m
$d = 5$ mm (with the factor 1.22 it is about 6 mm, still of the order of a few mm).
So the minimum resolvable distance is of the order of 5 mm.